From quantifier depth to quantifier number: Separating structures with k variables
H Vinall-Smeeth - Proceedings of the 39th Annual ACM/IEEE …, 2024 - dl.acm.org
Given two n-element structures, A and ℬ, which can be distinguished by a sentence of k-
variable first-order logic (ℒk), what is the minimum f (n) such that there is guaranteed to be a …
variable first-order logic (ℒk), what is the minimum f (n) such that there is guaranteed to be a …
Succinctness of Cosafety Fragments of LTL via Combinatorial Proof Systems (extended version)
This paper focuses on succinctness results for fragments of Linear Temporal Logic with Past
(LTL) devoid of binary temporal operators like until, and provides methods to establish them …
(LTL) devoid of binary temporal operators like until, and provides methods to establish them …
Multi-Structural Games and Beyond
Multi-structural (MS) games are combinatorial games that capture the number of quantifiers
of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht …
of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht …
Game characterizations for the number of quantifiers
L Hella, K Luosto - Mathematical Structures in Computer Science, 2024 - cambridge.org
A game that characterizes equivalence of structures with respect to all first-order sentences
containing a given number of quantifiers was introduced by Immerman in 1981. We define …
containing a given number of quantifiers was introduced by Immerman in 1981. We define …
Succinctness of Cosafety Fragments of LTL via Combinatorial Proof Systems
This paper focuses on succinctness results for fragments of Linear Temporal Logic with Past
(LTL) devoid of binary temporal operators like until, and provides methods to establish them …
(LTL) devoid of binary temporal operators like until, and provides methods to establish them …
On the number of quantifiers needed to define boolean functions
The number of quantifiers needed to express first-order (FO) properties is captured by two-
player combinatorial games called multi-structural games. We analyze these games on …
player combinatorial games called multi-structural games. We analyze these games on …
Parallel Play Saves Quantifiers
The number of quantifiers needed to express first-order properties is captured by two-player
combinatorial games called multi-structural (MS) games. We play these games on linear …
combinatorial games called multi-structural (MS) games. We play these games on linear …
Description Complexity of Unary Structures in First-Order Logic with Links to Entropy
R Jaakkola, A Kuusisto, M Vilander - arXiv preprint arXiv:2406.02108, 2024 - arxiv.org
The description complexity of a model is the length of the shortest formula that defines the
model. We study the description complexity of unary structures in first-order logic FO, also …
model. We study the description complexity of unary structures in first-order logic FO, also …
Boolean basis, formula size, and number of modal operators
C Berkholz, D Kuske, C Schwarz - arXiv preprint arXiv:2408.11651, 2024 - arxiv.org
Is it possible to write significantly smaller formulae when using Boolean operators other than
those of the De Morgan basis (and, or, not, and the constants)? For propositional logic, a …
those of the De Morgan basis (and, or, not, and the constants)? For propositional logic, a …